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2014 Binary frames, graphs and erasures
Bernhard Bodmann, Bijan Camp, Dax Mahoney
Involve 7(2): 151-169 (2014). DOI: 10.2140/involve.2014.7.151

Abstract

This paper examines binary codes from a frame-theoretic viewpoint. Binary Parseval frames have convenient encoding and decoding maps. We characterize binary Parseval frames that are robust to one or two erasures. These characterizations are given in terms of the associated Gram matrix and with graph-theoretic conditions. We illustrate these results with frames in lowest dimensions that are robust to one or two erasures. In addition, we present necessary conditions for correcting a larger number of erasures. As in a previous paper, we emphasize in which ways the binary theory differs from the theory of frames for real and complex Hilbert spaces.

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Bernhard Bodmann. Bijan Camp. Dax Mahoney. "Binary frames, graphs and erasures." Involve 7 (2) 151 - 169, 2014. https://doi.org/10.2140/involve.2014.7.151

Information

Received: 25 June 2012; Revised: 14 September 2012; Accepted: 14 September 2012; Published: 2014
First available in Project Euclid: 20 December 2017

zbMATH: 1286.42042
MathSciNet: MR3133716
Digital Object Identifier: 10.2140/involve.2014.7.151

Subjects:
Primary: 42C15
Secondary: 05C50, 94B05

Rights: Copyright © 2014 Mathematical Sciences Publishers

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Vol.7 • No. 2 • 2014
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